Multiply the following complex numbers: $({-4-5i}) \cdot ({i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4-5i}) \cdot ({i}) = $ $ ({-4} \cdot {0}) + ({-4} \cdot {1}i) + ({-5}i \cdot {0}) + ({-5}i \cdot {1}i) $ Then simplify the terms: $ (0) + (-4i) + (0i) + (-5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (-4 + 0)i - 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (-4 + 0)i - (-5) $ The result is simplified: $ (0 + 5) + (-4i) = 5-4i $